Displaying similar documents to “Are most measurable functions one-to-one?”

On the open-open game

Peg Daniels, Kenneth Kunen, Haoxuan Zhou (1994)

Fundamenta Mathematicae

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We modify a game due to Berner and Juhász to get what we call “the open-open game (of length ω)”: a round consists of player I choosing a nonempty open subset of a space X and II choosing a nonempty open subset of I’s choice; I wins if the union of II’s open sets is dense in X, otherwise II wins. This game is of interest for ccc spaces. It can be translated into a game on partial orders (trees and Boolean algebras, for example). We present basic results and various conditions under which...

A survey on topological games and their applications in analysis.

Jiling Cao, Warren B. Moors (2006)

RACSAM

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In this survey article we shall summarise some of the recent progress that has occurred in the study of topological games as well as their applications to abstract analysis. The topics given here do not necessarily represent the most important problems from the area of topological games, but rather, they represent a selection of problems that are of interest to the authors.

A dichotomy on Schreier sets

Robert Judd (1999)

Studia Mathematica

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We show that the Schreier sets S α ( α < ω 1 ) have the following dichotomy property. For every hereditary collection ℱ of finite subsets of ℱ, either there exists infinite M = ( m i ) i = 1 ∞ ⊆ ℕ such that S α ( M ) = m i : i ∈ E : E ∈ S α ⊆ ℱ , or there exist infinite M = ( m i ) i = 1 ∞ , N ⊆ ℕ such that ℱ [ N ] ( M ) = m i : i ∈ F : F ∈ ℱ a n d F ⊂ N ⊆ S α .